Don Johnson's Website

My Personal 'Stuff'
Childrens'
Ages
Puzzle

A man knocks on the door of a house, and tells the woman who answers that he is doing a survey on the need for school places for children.   He asks if there are any children living at that address, and the woman tells him that there are three.

He then enquires the ages of the children, and the woman - who is fed up with being questioned by  bureaucrats - tells him that their ages, when multiplied together, gives 36.  

The man says that this is not enough information, so the woman tells him that their ages, when added, gives the number of the house next door.

The man looks at the next door house number, but after thinking for a moment, says that he still has insufficient information.

The woman says that the last thing she will say is that the eldest child is not at home.

"Ah!" says the man, who then writes down the ages of the children on his clipboard

What are the ages of the children ?

Now, don't cheat and scroll down to the answer until you have used your simple arithmetic and logic to work out the ages!

"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"

Solution to Childrens' Ages Puzzle

Possible ages for the children are:
36, 1, 1
18, 2, 1
12, 3, 1
9,   4, 1
9,   2, 2
6,   6, 1
6,   3, 2

These add up to:  38, 21, 16, 14, 13, 13, 11 respectively

If the number of the house next door had been 38, 21, 16, 14, or 11
then the ages of the children would have been known to the man,
but he said 'Not sufficient information' - so the house must have been # 13
(as there are two alternative sets of ages adding to 13)

When the woman said 'The eldest is not at home', this means there IS an eldest child,
so the children could not have been 6, 6 , 1 as there is not one  'eldest' with twins,
therefore:

The ages are 9, 2, 2


Did you get them right ?

Easy wasn't it?